J.P. Morgan Chase & Co. is willing to pay a steep price to settle with the Justice Department over soured mortgage securities, but it is getting one thing it wanted: It won't have to pay heavy penalties for the sins of two companies it bought during the financial crisis.

Under the terms of a tentative $13 billion deal that could be finalized in a matter of days, J.P. Morgan will pay roughly $2 billion in penalties that apply to its own conduct during the years before the financial crisis, and not any for problems it...